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I'm not sure how to calculate the odds for this:

There's a small raffle with 10 tickets sold. 3 of the tickets will win a prize. I've bought exactly 5 tickets. What are my odds of winning at least one prize? What is the formula?

It's not simply 1 in 2 (5 out of 10) because there's more than one prize.

Or more generally, what are my odds of winning an N ticket raffle, with M prizes offered when I buy X tickets?

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Your chance of not winning on the first ticket is $\frac 5{10}$ because there are five other tickets than yours. Assuming you lose the first, your chance of losing the second is $\frac 49$ and assuming you lose that your chance of losing the third is $\frac 38$. Your chance of winning at least one prize is $1$ minus the product of these $$1-\frac 5{10}\cdot \frac 49 \cdot \frac 38=\frac {11}{12}$$

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  • $\begingroup$ I'm sure this is correct. Can you generalize a formula? $\endgroup$
    – Octopus
    Mar 4, 2021 at 5:43
  • $\begingroup$ You haven't specified what generalization you are looking for. I suggest you understand the approach and apply it to your other problems. $\endgroup$ Mar 4, 2021 at 5:44
  • $\begingroup$ from the updated question, "...what are my odds of winning an N ticket raffle, with M prizes offered when I buy X tickets?" Isn't that the generalization I am looking for? $\endgroup$
    – Octopus
    Mar 4, 2021 at 5:46

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